Nonlinear spline adaptive filtering

In this paper a new class of nonlinear adaptive filters, consisting of a linear combiner followed by a flexible memory-less function, is presented. The nonlinear function involved in the adaptation process is based on a spline function that can be modified during learning. The spline control points are adaptively changed using gradient-based techniques. B-splines and Catmull-Rom splines are used, because they allow to impose simple constraints on control parameters. This new kind of adaptive function is then applied to the output of a linear adaptive filter and it is used for the identification of Wiener-type nonlinear systems. In addition, we derive a simple form of the adaptation algorithm and an upper bound on the choice of the step-size. Some experimental results are also presented to demonstrate the effectiveness of the proposed method.

► We propose a nonlinear filtering approach based on spline nonlinear functions.
► The proposed approach can solve the identification of nonlinear Wiener systems.
► The proposed approach outperforms other approaches based on Volterra filters.
► The proposed approach is characterized by a fast convergence speed.
► We derive an upper bound on the choice of the learning rate.